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Aug 2, 2017 · The boundary of a set is the set of limit points, that is, points such that there is a sequence of points in the set converging to them, intersected with the closure of its complement. Alternatively, it is the closure minus the interior. This question has got 4 answer in a row and all 4 are wrong. I am impressed.
Apr 20, 2014 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have
A sequence {an} {a n} is a bounded sequence if it is bounded above and bounded below. If a sequence is not bounded, it is an unbounded sequence. For example, the sequence {1 n} {1 n} is bounded above because 1 n ≤1 1 n ≤ 1 for all positive integers n n. It is also bounded below because 1 n ≥0 1 n ≥ 0 for all positive integers n.
Feb 21, 2015 · No,it's fine. If you have the zero sequence {an} {a n} then for every M> 0 M> 0 you have an ≤ M a n ≤ M. We define M> 0 M> 0 so we can use it sometimes to a fraction like ,let ϵ = 1 M ϵ = 1 M. etc... To have a more concrete bound: The zero sequence is bounded by M = 1 M = 1.
May 28, 2014 · And I discovered that you can do the same type of number sequence starting with a different number. For example, we can call this one “Jinny’s Sequence”. 3, 3, 6, 9, 15, 24, 39, 63, 102, 165, etc. Once again, by the time you get to the 10 th number, and divide the 10 th by the 9 th you get very close to the Golden Ratio….1.6176
One way to describe an ordered list of numbers is as a sequence. A sequence is a function whose domain is a subset of the counting numbers. The sequence established by the number of hits on the website is \(\{ 2,4,8,16,32,…\}\) The ellipsis (…) indicates that the sequence continues indefinitely. Each number in the sequence is called a term.
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The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.
